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Crypto Clustering

This program utilizes financial Python programming and unsupervised learning to cluster cryptocurrencies based on their performance in different time periods, utilizing K-Means and Principal Component Analysis (PCA). The dataset used in this analysis is a CSV file containing returns (price change) data of cryptocurrencies across various periods.

The analysis process is divided into the following steps:

Data import Data preparation Determining the optimal value of 'k' using the original dataset Cryptocurrency clustering with K-means using the original dataset Optimization of clusters using Principal Component Analysis Determining the optimal value of 'k' using the PCA dataset Cryptocurrency clustering with K-means using the PCA dataset Visualization and comparison of results. Overall, this code is designed to cluster cryptocurrencies in a structured and systematic manner, using a combination of financial Python programming and unsupervised learning techniques, in order to gain insights into their performance in different time periods.

# dependencies and setup
from package.constants import * # constants
from package.helpers import * # libraries, dependencies and functions

# Import required libraries and dependencies
import pandas as pd

import hvplot.pandas
from sklearn.cluster import KMeans
from sklearn.decomposition import PCA
from sklearn.preprocessing import StandardScaler

Prepare the Data

# Load the data into a Pandas DataFrame
df_market_data = pd.read_csv(DATA_URL+"crypto_market_data.csv", index_col="coin_id")

# Display sample data
df_market_data.head()

	price_change_percentage_24h	price_change_percentage_7d	price_change_percentage_14d	price_change_percentage_30d	price_change_percentage_60d	price_change_percentage_200d	price_change_percentage_1y
coin_id
bitcoin	1.08388	7.60278	6.57509	7.67258	-3.25185	83.51840	37.51761
ethereum	0.22392	10.38134	4.80849	0.13169	-12.88890	186.77418	101.96023
tether	-0.21173	0.04935	0.00640	-0.04237	0.28037	-0.00542	0.01954
ripple	-0.37819	-0.60926	2.24984	0.23455	-17.55245	39.53888	-16.60193
bitcoin-cash	2.90585	17.09717	14.75334	15.74903	-13.71793	21.66042	14.49384

# Generate the DF info
df_market_data.info()

<class 'pandas.core.frame.DataFrame'>
Index: 41 entries, bitcoin to digibyte
Data columns (total 7 columns):
 #   Column                        Non-Null Count  Dtype  
---  ------                        --------------  -----  
 0   price_change_percentage_24h   41 non-null     float64
 1   price_change_percentage_7d    41 non-null     float64
 2   price_change_percentage_14d   41 non-null     float64
 3   price_change_percentage_30d   41 non-null     float64
 4   price_change_percentage_60d   41 non-null     float64
 5   price_change_percentage_200d  41 non-null     float64
 6   price_change_percentage_1y    41 non-null     float64
dtypes: float64(7)
memory usage: 2.6+ KB

# Generate the summary statistics
df_market_data.describe(include = 'all').round(2)

	price_change_percentage_24h	price_change_percentage_7d	price_change_percentage_14d	price_change_percentage_30d	price_change_percentage_60d	price_change_percentage_200d	price_change_percentage_1y
count	41.00	41.00	41.00	41.00	41.00	41.00	41.00
mean	-0.27	4.50	0.19	1.55	-0.09	236.54	347.67
std	2.69	6.38	8.38	26.34	47.37	435.23	1247.84
min	-13.53	-6.09	-18.16	-34.71	-44.82	-0.39	-17.57
25%	-0.61	0.05	-5.03	-10.44	-25.91	21.66	0.41
50%	-0.06	3.30	0.11	-0.04	-7.54	83.91	69.69
75%	0.61	7.60	5.51	4.58	0.66	216.18	168.37
max	4.84	20.69	24.24	140.80	223.06	2227.93	7852.09

line(df_market_data,"Price Change Over Time")

# Use the StandardScaler() module to normalize the data from the CSV file
data_scaled = StandardScaler().fit_transform(df_market_data)
# Create a DF for the scaled data
df_market_scaled = pd.DataFrame(data_scaled, columns=df_market_data.columns, index=df_market_data.index)
df_market_scaled.head()

	price_change_percentage_24h	price_change_percentage_7d	price_change_percentage_14d	price_change_percentage_30d	price_change_percentage_60d	price_change_percentage_200d	price_change_percentage_1y
coin_id
bitcoin	0.508529	0.493193	0.772200	0.235460	-0.067495	-0.355953	-0.251637
ethereum	0.185446	0.934445	0.558692	-0.054341	-0.273483	-0.115759	-0.199352
tether	0.021774	-0.706337	-0.021680	-0.061030	0.008005	-0.550247	-0.282061
ripple	-0.040764	-0.810928	0.249458	-0.050388	-0.373164	-0.458259	-0.295546
bitcoin-cash	1.193036	2.000959	1.760610	0.545842	-0.291203	-0.499848	-0.270317

df_market_scaled.describe(include = 'all').round(2)

	price_change_percentage_24h	price_change_percentage_7d	price_change_percentage_14d	price_change_percentage_30d	price_change_percentage_60d	price_change_percentage_200d	price_change_percentage_1y
count	41.00	41.00	41.00	41.00	41.00	41.00	41.00
mean	0.00	0.00	0.00	0.00	0.00	-0.00	0.00
std	1.01	1.01	1.01	1.01	1.01	1.01	1.01
min	-4.98	-1.68	-2.22	-1.39	-0.96	-0.55	-0.30
25%	-0.13	-0.71	-0.63	-0.46	-0.55	-0.50	-0.28
50%	0.08	-0.19	-0.01	-0.06	-0.16	-0.36	-0.23
75%	0.33	0.49	0.64	0.12	0.02	-0.05	-0.15
max	1.92	2.57	2.91	5.35	4.77	4.63	6.09

line(df_market_scaled,"Standardized Price Change Over Time")

from sklearn.cluster import KMeans
km = KMeans(n_clusters = 4, n_init = 25, random_state = 1234)

km.fit(df_market_scaled)

KMeans(n_clusters=4, n_init=25, random_state=1234)

km.labels_

array([0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0,
       1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 2, 0, 1, 1, 3, 1, 1, 1, 1])

km.inertia_

79.02243535120977

pd.Series(km.labels_).value_counts().sort_index()

0    13
1    26
2     1
3     1
dtype: int64

km.cluster_centers_

array([[ 0.23756041,  1.19101578,  0.83462785,  0.19065425, -0.212313  ,
        -0.22264199, -0.20800783],
       [ 0.03258562, -0.56998841, -0.4827023 , -0.25453208, -0.07913767,
        -0.18795807, -0.18203893],
       [-4.98104189, -0.04517829, -1.20695612, -1.21212587,  0.04773554,
         4.63238025,  6.08862545],
       [ 1.04553034, -0.61832816,  2.90705393,  5.35145461,  4.76991278,
         3.14887546,  1.34848839]])

cluster_centers = pd.DataFrame(km.cluster_centers_, columns=df_market_data.columns)
cluster_centers

	price_change_percentage_24h	price_change_percentage_7d	price_change_percentage_14d	price_change_percentage_30d	price_change_percentage_60d	price_change_percentage_200d	price_change_percentage_1y
0	0.237560	1.191016	0.834628	0.190654	-0.212313	-0.222642	-0.208008
1	0.032586	-0.569988	-0.482702	-0.254532	-0.079138	-0.187958	-0.182039
2	-4.981042	-0.045178	-1.206956	-1.212126	0.047736	4.632380	6.088625
3	1.045530	-0.618328	2.907054	5.351455	4.769913	3.148875	1.348488

import plotly.graph_objs as go  # Import the plotly library

# Create the trace for the data points
trace_points = go.Scatter(
    x=df_market_scaled['price_change_percentage_24h'],
    y=df_market_scaled['price_change_percentage_7d'],
    mode='markers',
    name='Coins',
    marker=dict(
        size=12.5,
        color=km.labels_,
        colorscale=["blue", "yellow", "red","green"],
        opacity=0.9,
        line=dict(
            width=1,
            color='black'
        )
    ),
    text=df_market_scaled.index  # Set the hover text to the index value
)

# Create the trace for the centroid points
trace_centroids = go.Scatter(
    x=cluster_centers['price_change_percentage_24h'],
    y=cluster_centers['price_change_percentage_7d'],
    mode='markers',
    name='Cluster Centers',
    marker=dict(
        size=25,
        color=cluster_centers.index,
        colorscale=["blue", "yellow", "red","green"],
        symbol='diamond',
        opacity=0.5,
        line=dict(
            width=1,
            color='black'
        )
    ),
    text=[f"Centroid {i}" for i in range(len(cluster_centers))]  # Set the hover text to "Centroid {i}"
)

# Define the layout of the plot
layout = go.Layout(
    legend=dict(
        yanchor="top",
        y=0.99,
        xanchor="left",
        x=0.01,
        bgcolor= '#f7f7f7',
        font=dict(color='black', size=14)

),
    width=800,
    height=800,
    title=dict(text="GO Plot",
              font=dict(size= 24, color= 'black'),
              x=0.5,
              y=0.91),
    xaxis=dict(title='Price Change Percentage 24h',
              showline=True,
        linewidth=1.5,
        linecolor='black',
        mirror=True,
              color= 'black',
               gridcolor='white'),
    yaxis=dict(title='Price Change Percentage 7d',
               showline=True,
               linewidth=1.5,
               linecolor='black',
               mirror=True,
               color= 'black',
               gridcolor='white'),
    hovermode='closest',
    plot_bgcolor='#ffffff',
    paper_bgcolor="#f7f7f7"
)

# Create the figure object and add the traces to it
fig = go.Figure(data=[trace_points, trace_centroids], layout=layout)

# Show the figure
fig.show()

from sklearn.cluster import AgglomerativeClustering
cluster = AgglomerativeClustering(n_clusters=5, affinity='euclidean', linkage='ward')  
labels = cluster.fit_predict(df_market_scaled)

df = pd.DataFrame(df_market_scaled, columns=['price_change_percentage_24h', 'price_change_percentage_7d',
                               'price_change_percentage_14d', 'price_change_percentage_30d',
                               'price_change_percentage_60d', 'price_change_percentage_200d',
                               'price_change_percentage_1y'])
df['cluster'] = labels

# calculate the mean values for each cluster
cluster_centers = df.groupby('cluster').mean()
cluster_centers

	price_change_percentage_24h	price_change_percentage_7d	price_change_percentage_14d	price_change_percentage_30d	price_change_percentage_60d	price_change_percentage_200d	price_change_percentage_1y
cluster
0	0.001893	-0.815288	-1.225777	-0.370342	0.000158	0.226629	-0.065063
1	0.074391	-0.096739	0.147830	-0.100759	-0.201319	-0.414732	-0.249308
2	-4.981042	-0.045178	-1.206956	-1.212126	0.047736	4.632380	6.088625
3	1.045530	-0.618328	2.907054	5.351455	4.769913	3.148875	1.348488
4	0.367596	1.840230	1.192931	0.313590	-0.031483	-0.084783	-0.175400

plt.figure(figsize=(10, 8))

ax = sns.scatterplot(data = df_market_scaled,
                     x = 'price_change_percentage_24h',
                     y = 'price_change_percentage_7d', 
                     hue = cluster.labels_, 
                     palette = "bright", 
                     alpha = 0.8, 
                     s = 150,
                     legend = False)
#Plot the Centroids
ax = sns.scatterplot(data = cluster_centers, 
                     x = 'price_change_percentage_24h',
                     y = 'price_change_percentage_7d', 
                     hue = cluster_centers.index, 
                     palette = 'colorblind', 
                     alpha = 0.4, 
                     s = 600,
                     marker = 'D',
                     ec = 'black', 
                     legend = False)

# Add Centroid Labels
for i in range(len(cluster_centers)):
               plt.text(x = cluster_centers.price_change_percentage_24h[i], 
                        y = cluster_centers.price_change_percentage_7d[i],
                        s = i, 
                        horizontalalignment='center',
                        verticalalignment='center',
                        size = 15,
                        alpha = 0.4,
                        weight = 'bold',
                        color = 'k')

The Within Cluster Sum of Squares (WCSS)

wcss = []
for k in range(2, 11):
    km = KMeans(n_clusters = k, n_init = 25, random_state = 1234)
    km.fit(df_market_scaled)
    wcss.append(km.inertia_)

wcss_series = pd.Series(wcss, index = range(2, 11))

plt.figure(figsize=(8, 6))
ax = sns.lineplot(y = wcss_series, x = wcss_series.index)
ax = sns.scatterplot(y = wcss_series, x = wcss_series.index, s = 150)
ax = ax.set(xlabel = 'Number of Clusters (k)', 
            ylabel = 'Within Cluster Sum of Squares (WCSS)')

The Average Silhouette Score

from sklearn.metrics import silhouette_score

silhouette = []
for k in range(2, 11):
    km = KMeans(n_clusters = k, n_init = 25, random_state = 1234)
    km.fit(df_market_scaled)
    silhouette.append(silhouette_score(df_market_scaled, km.labels_))

silhouette_series = pd.Series(silhouette, index = range(2, 11))

plt.figure(figsize=(8, 6))
ax = sns.lineplot(y = silhouette_series, x = silhouette_series.index)
ax = sns.scatterplot(y = silhouette_series, x = silhouette_series.index, s = 150)
ax = ax.set(xlabel = 'Number of Clusters (k)', 
            ylabel = 'Average Silhouette Score')

The Calinski Harabasz Score

from sklearn.metrics import calinski_harabasz_score

calinski = []
for k in range(2, 11):
    km = KMeans(n_clusters = k, n_init = 25, random_state = 1234)
    km.fit(df_market_scaled)
    calinski.append(calinski_harabasz_score(df_market_scaled, km.labels_))

calinski_series = pd.Series(calinski, index = range(2, 11))

plt.figure(figsize=(8, 6))
ax = sns.lineplot(y = calinski_series, x = calinski_series.index)
ax = sns.scatterplot(y = calinski_series, x = calinski_series.index, s = 150)
ax = ax.set(xlabel = 'Number of Clusters (k)', 
            ylabel = 'Calinski Harabasz Score')

Find the Best Value for k Using the OG Data

Question 1: What is the best k?

It looks like 4 is the best value of k!

---

Optimize Clusters with Principal Component Analysis

# Create a PCA model instance and set n_components = 3
pca=PCA(n_components=3)
# Use the PCA model with `fit_transform` to reduce to 
# three principal components.
df_market_pca =pd.DataFrame(pca.fit_transform(df_market_scaled)).head(5)
# View the first five rows of the DataFrame.
df_market_pca

	0	1	2
0	-0.600667	0.842760	0.461595
1	-0.458261	0.458466	0.952877
2	-0.433070	-0.168126	-0.641752
3	-0.471835	-0.222660	-0.479053
4	-1.157800	2.041209	1.859715

# Retrieve the explained variance to determine how much information 
# can be attributed to each principal component.
pca.explained_variance_ratio_

array([0.3719856 , 0.34700813, 0.17603793])

sum(pca.explained_variance_ratio_)

0.8950316570309841

Together, the two principal components contain about 96% of the information. The first principal component contains about 73% of the variance. The second principal component contains about 23% of the variance.

Question 2: What is the total variance of the three principal componenets?

# Create column names for the PCA components
pca_columns = ['PCA{}'.format(i) for i in range(1, 4)]

# Perform PCA on the scaled data and create a DataFrame with the results
pca = PCA(n_components=3)
market_pca = pca.fit_transform(df_market_scaled)
market_pca_df = pd.DataFrame(market_pca, columns=pca_columns, index=df_market_data.index)

# Display the first few rows of the DataFrame
market_pca_df.head()

	PCA1	PCA2	PCA3
coin_id
bitcoin	-0.600667	0.842760	0.461595
ethereum	-0.458261	0.458466	0.952877
tether	-0.433070	-0.168126	-0.641752
ripple	-0.471835	-0.222660	-0.479053
bitcoin-cash	-1.157800	2.041209	1.859715

inertia = []
# Append the value of the computed inertia from the `inertia_` attribute of teh KMeans model instance
for k in range(2, 11):
    k_model = KMeans(n_clusters=k, random_state=1)
    k_model.fit(market_pca_df)
    inertia.append(k_model.inertia_)

# Define a DataFrame to hold the values for k and the corresponding inertia
elbow_data = {"k": range(2, 11), "inertia": inertia}
df_elbow = pd.DataFrame(elbow_data)

# Review the DataFrame
df_elbow.head()

plt.figure(figsize=(8, 6))
ax = sns.lineplot(y = df_elbow["inertia"], x = df_elbow["k"])
ax = sns.scatterplot(y =  df_elbow["inertia"], x = df_elbow["k"], s = 150)
ax = ax.set(xlabel = 'Number of Clusters (k)', 
            ylabel = 'Within Cluster Sum of Squares (WCSS)')
plt.axvline(x=4, color='k', linestyle='--')

<matplotlib.lines.Line2D at 0x14410f8a6d0>

model = KMeans(n_clusters=4, random_state=0)

# Fit the model
model.fit(market_pca_df)

# Make predictions
k_3 = model.predict(market_pca_df)

# Create a copy of the PCA DataFrame
market_pca_df_predictions_df = market_pca_df.copy()

# Add a class column with the labels
market_pca_df_predictions_df["segments"] = k_3
market_pca_df_predictions_df

	PCA1	PCA2	PCA3	segments
coin_id
bitcoin	-0.600667	0.842760	0.461595	0
ethereum	-0.458261	0.458466	0.952877	0
tether	-0.433070	-0.168126	-0.641752	3
ripple	-0.471835	-0.222660	-0.479053	3
bitcoin-cash	-1.157800	2.041209	1.859715	0
binancecoin	-0.516534	1.388377	0.804071	0
chainlink	-0.450711	0.517699	2.846143	0
cardano	-0.345600	0.729439	1.478013	0
litecoin	-0.649468	0.432165	0.600303	0
bitcoin-cash-sv	-0.759014	-0.201200	-0.217653	3
crypto-com-chain	-0.248198	-1.376252	-1.462026	3
usd-coin	-0.438408	-0.175337	-0.663388	3
eos	-0.693425	-0.473815	-0.527597	3
monero	0.060499	2.909404	1.498571	0
tron	-0.393352	-0.108192	-0.012756	3
tezos	-0.796176	-0.494409	1.082812	0
okb	0.064075	-1.269825	-1.098829	3
stellar	-0.489015	-0.732719	-0.062543	3
cosmos	-0.306272	0.703415	1.714224	0
cdai	-0.513528	-0.142802	-0.656566	3
neo	-0.362120	-0.986914	-0.728752	3
wrapped-bitcoin	-0.604265	0.827398	0.439316	0
leo-token	-0.413296	-0.674115	-1.076628	3
huobi-token	-0.407483	-0.212507	-0.351426	3
nem	0.608974	0.563532	-1.148742	3
binance-usd	-0.450211	-0.151019	-0.647401	3
iota	-0.764665	-0.517886	0.204990	3
vechain	-0.556315	-1.938209	-1.261776	3
zcash	-0.425147	0.492976	1.058048	0
theta-token	2.676868	-0.013954	-1.965207	3
dash	-0.613923	-0.479337	0.339565	3
ethereum-classic	-0.579924	-0.356334	-0.114942	3
ethlend	8.089018	-3.896891	2.301382	1
maker	-0.389045	0.165041	0.379414	0
havven	0.865762	-2.261882	0.275583	3
omisego	0.111675	0.428316	-1.205398	3
celsius-degree-token	4.792395	6.767679	-1.986985	2
ontology	-0.632355	-2.108117	-0.652227	3
ftx-token	-0.593142	0.021485	0.209911	3
true-usd	-0.458131	-0.135734	-0.635284	3
digibyte	-0.297910	-0.191126	-0.909602	3

 # Plot the clusters
market_pca_df_predictions_df.hvplot.scatter(
    x="PCA2",
    y="PCA3",
    by="segments"
)

Find the Best Value for k Using the PCA Data

PCA Elbow Plot!

Question 3: What is the best value of k when using the PCA data?

The best k value is 4!

Question 4: Does it differ from the best k value found using the original data?

The best value of k for both the original and pca data are the same! However, the elbow curve for the pca data has been translated down (smaller y-intercept) meaning that the inertia is lower for the pca k values.

Cluster Cryptocurrencies with K-means Using the PCA Data

# Initialize the kmeans model
# Fit the model with the market pca data
# Store the predictions
model_pca = KMeans(n_clusters=4)
model_pca.fit(market_pca_df)
predictions_pca = model_pca.predict(market_pca_df)

predictions_pca

array([0, 0, 3, 3, 0, 0, 0, 0, 0, 3, 3, 3, 3, 0, 3, 0, 3, 3, 0, 3, 3, 0,
       3, 3, 3, 3, 3, 3, 0, 3, 3, 3, 1, 0, 3, 3, 2, 3, 3, 3, 3])

# Make a copy of the market df (NOT pca)
# Make a column for the predictions using the pca data
# Will compare clusters
df_market_pca_predictions = df_market_predictions.copy()
df_market_pca_predictions["predictions_pca"] = predictions_pca
df_market_pca_predictions.head(5)

# Make a copy of the market pca df
df_pca_predictions = market_pca_df.copy()
df_pca_predictions["predictions_pca"] = predictions_pca
df_pca_predictions.index = i
df_pca_predictions.head(5)

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
~\AppData\Local\Temp\ipykernel_19372\928028864.py in <module>
      2 # Make a column for the predictions using the pca data
      3 # Will compare clusters
----> 4 df_market_pca_predictions = df_market_predictions.copy()
      5 df_market_pca_predictions["predictions_pca"] = predictions_pca
      6 df_market_pca_predictions.head(5)

NameError: name 'df_market_predictions' is not defined

Plot the clusters!

clusters_pca = df_market_pca_predictions.hvplot.scatter(
    x = "price_change_percentage_24h",
    y = "price_change_percentage_7d",
    by = "predictions_pca",
    hover_cols = 'index'
)
clusters_pca

Visualize and Compare Results

elbow_og * elbow_pca

clusters_og * clusters_pca

Question: Based on visually analyzing the cluster analysis results, what’s the impact of using fewer features to cluster the data by using K-means?

I don't actually see a difference! The predictions for both were the same in this case.

Below are plots as required by the "instructions" that I think are in error

# Composition of the elbow plots 
elbow_og + elbow_pca

# Composition of the scatter plots
clusters_og+clusters_pca

Extra Analysis

#plot dendogram. If we cut at y=17, we get 5 clusters
from scipy.cluster import hierarchy as sch
plt.figure(figsize=(10, 7))  
plt.title("Dendrograms")
dend3 = sch.dendrogram(sch.linkage(df_market_scaled, method='ward'))
plt.xticks(rotation=90)
plt.gca().set_xticklabels(df_market_scaled.index[dend3['leaves']])
plt.axhline(y=6, color='k', linestyle='--')